As someone who ran 7/8" manilla wire core flip-lines for a couple decades I would recommend you think about going with 3/4" instead...You will feel very little difference between the 3/4" and the 7/8", and it is fairly easy to get a rope grab that will handle the 3/4" rope. With the 7/8" you are most likely gonna be using a becket hitch on your side dee which is a royal pain in the ass compared to a more modern setup...I would also consider going straight 3 strand with no cable...Super strong. Can splice an eye on one end and a back splice on the other in about 5 minutes. Cheap and very easy to find. Won't rot like manilla. Rolls up tree better than anything I have ever used.
https://www.wesspur.com/items/pm3415.html
I have seen 3 men fall out trees because they cut their flip-line and all 3 were using wire-core...The myth that wire-core is gonna save your life if you do something really stupid is just that... A myth....